hint: for the ball to reach the ground without hitting the rock, the condition is that the y-coordinate of ball should be greater than a certain height.
placing the origin at the center of sphere, ##R^2=x^2+y^2##
##(x,y)## are coordinates on the surface of hemisphere
use kinematic...
The x-direction used is clearly along the ramp with positive direction going up along the ramp, I hope you are not confused about how the x-y coordinate system is defined in the given solution. You might want to draw a free body diagram to clear things up. When you take component of forces along...
It's about the places of error, here the error doesn't exist in the thousand's place. Hundred's place is uncertain in spite of the fact that it is significant!!!
I hope this helps!!!
Edit: It always helps to write in scientific notation.....usually after rounding off its written as...
Your solution seems fine for "work done by you". "work done by friction" would be negative of the calculated value. Also note that your answer should have only two significant figures. That means answer should have been ##2.0~kJ##. This could be the reason you were marked down.
That assumption isn't correct. The given velocity in the question is the initial velocity. And it stops after 6 seconds. Acceleration would be negative. And it seems you did take that into account in the final equation, otherwise the answer wouldn't be correct. Yes, the answer is correct. But be...
no problem!!!.........just to make it seem reasonable you can use ##v=v_{0}+a.t##, solving for time gives ##10~seconds##. It doesn't stop immediately, it slowly decelerates therefore time is comparatively large and so is the distance. I hope this makes more sense now!!!!
does it?....check your final equation, you have done the rest of it correctly....it should be -ve because of deceleration (retardation), it just shows acceleration acts in direction opposite to its initial velocity
##0=6+2a##
##a=-3##
Edit: I think it was a typo, but this is what the equation...
time would depend on the initial net acceleration. It would help if you draw free body diagram and check the net force acting on body. Would the net force depend on slope of incline???.---------->The correct answer to this question would answer your question.
Caution: They all will have same...
I believe its the "bearing" term that is the cause of problem. I quote Wikipedia :
what haruspex meant was that direction of velocity of A and displacement vector from A to B has angle zero between them. I hope this helps!!!
yeah, my mistake for overlooking that!!!...edited the original post....thanks for pointing that out!!!.....btw I meant backward but wrote forward the rest of it was correct....silly me!!!:redface:
But you get the point, the ball will eventually start to roll. If translation kinetic energy is...
That relation is only valid for pure rolling (no sliding). You shouldn't calculate torque about ICR, if the body is accelerating (remember what I said previously about fictitious torque).
friction in this case(back spin case) would be kinetic. and after a while if friction is present then...
The answer to this is if an object of volume ##x## is submerged in water then the volume of water displaced is also ##x##. Can you figure this out now?
I believe you have taken the distance (moment arm) ##\frac{R}{4}## incorrectly.
Edit: I believe moment arm should be ##\frac{3R}{4}## if the distance (force is applied below COM) from COM is ##\frac{R}{4}##
you might wanna clear that out, instantaneous center of rotation is different from center of rotation (usually taken to be COM for rolling ball).
P is the instantaneous center of rotation whereas M is COM.
As I mentioned in my previous posts, use standard units. So,
Density of water is ##1.\frac{g}{cm^3}=1000.\frac{kg}{m^3}##
Read about SI units, so that you know which units to use when. And also check out "conversion using conversion factors" to be clear about conversion
In what units volume is measured???....Think hard and answer.
I believe you didn't read the question nor my post carefully, or you have some doubt about the equation itself!!!
$$F_{b}=ρ.V.g$$
What does the variables in the above equation represent????
Edit: For force to be in newtons, mass...
Numbers without units are meaningless, always indicate the units. Look always try to use standard units for calculation, other wise error creeps unknowingly sometimes. If you check carefully your units in answer of volume, units would be ##\frac{cm^3.kg}{g}##. Make adjustments so that units of...
I personally avoid non-inertial frame specially for rotation, sorry can't help you with that equation.
I mentally calculated torque about COM, and check the tendency of rotation if I increase the force beyond the balance condition.
it purely depends on the situation. This intuition develops...
You have not included fictitious torque!!!
First of all if friction isn't acting the block will topple backwards, so normal force would act along back edge. Try to see that, block can topple either way forward or backward.
Consider it a advice: Its always good to take torque about COM...
read the complete thing!!!!
it can topple backwards, without any frictional force whatsoever, it would just need a specific force for that to happen.
If friction isn't present then the body must be accelerating, right???.....if you take moment about point O, then you'll have to take...
Hey, Pranav!
The question doesn't mention how it topples. It topples on the front or the back edge depending on the conditions. Think about it this way, if it has to topple forward (fall towards front), then friction must be present but what about the back edge (fall backwards) and remember...